The first time we meet, Delfina Delettrez Fendi wears Delfina Delettrez, and Fendi. There's a multicoloured furry Fendi gewgaw dangling from her Fendi handbag. Her heels are Fendi, too, and she's bedecked in her own surrealistic jewellery designs, all enamelled pouting lips and lashed eyes. A trio of brooches – nose, eyes and mouth chained together – form a face over her heart. Miniature puckers and winks glitter at her ears and fingers. She ends up looking a bit like a walking Picasso portrait. I think she'd like the comparison.

Despite the outré accessories and jewellery, Delettrez's dress is spare, simple, vintage. It may be vintage Fendi – though I don't manhandle the label to check – but, stark to the point of austerity, it has something of the air of Wallis Simpson's wardrobe of Molyneux and Mainbocher from the Thirties, also foils for surrealist experiments in bizarre bijoux. Those are obvious references when you look at Delettrez's work, but while her jewellery contains glitter and gold, that's where their similarity to other gems ends.

Delettrez has inverted her diamonds to flaunt their underside, enamelled gold to resemble eyeballs, and crafted a slightly creepy silver exoskeleton to sit outside the hand. Even during its quieter moments, she goes for the extreme option: her gold, leaf-shaped earrings wriggle with enamelled insects, her honeycomb bracelets are coated with nectar-like resin, encrusted with life-size gold wasps.

Delettrez puts you in mind of another Italian surrealist: the designer Elsa Schiaparelli. It's not just because we meet at the Café de Flore in Paris during haute couture week, a few hours after Christian Lacroix has presented the first collection under the Schiaparelli label since 1954. Delettrez herself bears more than a passing resemblance to Schiap.

It's not just that her outfit is pockmarked with scarlet pouts, like that Schiaparelli suit smooched down the front with lipstick-kiss buttons, but her countenance and character, too. They both have strong, imperious noses, slightly downwards-turning mouths, and famous surnames. Elsa's uncle was the astronomer and Martian enthusiast, Giovanni Schiaparelli; Delfina Delettrez is, of course, also a Fendi, daughter of Silvia Venturini Fendi, current head of accessories at the family's house and inventor of the baguette handbag, the ubiquitous It-bag of the late Nineties.

I'm also put in mind of Lacroix's own definition of Schiaparelli's approach to fashion as a "laboratory of ideas". Especially as that's a word Delettrez herself uses. "I really needed to have my own laboratory. I've got a laboratory – it's craftsmen, an atelier. I call it a laboratory because what I do is experiment." The experiments come about because Delettrez doesn't have a jewellery background – nor fashion, when it comes to education.

Born in 1987, in Rome, and raised between Italy, Brazil and France, Delettrez originally studied costume design, albeit briefly. "I studied there just four months, because then I turned out pregnant," she states. "You have to do the same work as the actors and it's very physical so I had to quit. They don't want pregnant girls… but I was fascinated by all the psychology behind costume. I learnt to read a script and to identify with the characters' minds. It's the kind of thing I do even now."

It all sounds standard – many designers start out pursuing a different path before finding their feet in fashion: costume design and architecture being two favourite starting blocks. But then, Delettrez comments absent-mindedly, "I was even fascinated by what Fendi did for Fellini, Visconti, the relationship we always had with Italian cinema. But you know, I guess it wasn't my… it wasn't my turn." And you realise she's coming from a very different direction indeed.

Fendi was the word I wasn't certain I could mention, but Delettrez discusses her family with ease. That's the crux: we're used to seeing it stitched into the back of a dress, whereas for Delettrez, Fendi means family. Talk to her about handicraft, and she comments, "I was observing my mum's bags – the Selleria. And you've got the stitches, one smaller than the other, and to me that's the beauty of the mistake and that's the beauty of the imperfection." To the rest of the world, a Fendi handbag is a status-symbol, but for Delettrez it was just part of growing up.

Fendi is also, perhaps, one of the sources of Delettrez's strength. Originally founded in 1925 by Adele Casagrande (a Fendi by marriage), the house was propelled to prominence by her daughters, Paola, Franca, Carla, Alda and Anna, Delettrez's grandmother. It's a female fashion dynasty, a legacy of strong, forceful women in the terribly Italian mould. Delfina is just the latest in the lineage.

Delettrez models some of her striking jewellery, all of which is made by handDelettrez's comfort with discussing her fashion-famous family possibly comes from the simple fact that she has shrugged off any 'daughter of' allusions, just as she shrugged off the Fendi appellation from her label, launched in 2007. She was just 20, a new mother, with no formal jewellery training. The spark came when a pregnant Delettrez created a piece with a stone that had been given to her at birth, with the intention – eventually – of handing it on to her own daughter.

"Jewellery was passed from generation through generation in this very Italian way," says Delettrez. "Of course, my family are all women, we all love jewellery so I was really swamped… I loved to see how a piece could totally change your outfit and even your attitude, like for example my mother was wearing this Bulgari tubogas bracelet, and I was watching her body changing. She was more regal… I was really attracted by this."

Delettrez's first piece broke the rules straight away. "I put the stone upside down and [the craftsmen] were like 'Oh gosh!'," she says, with a laugh. "It's a dialogue, a constant dialogue, because I don't have this technical approach, but it's not a bad thing. Jewellery has these very ancient traditions and rules, so sometimes you feel very guilty. You feel you are doing something wrong if you twist them."

Delettrez's work consistently cocks a snook at convention: she retails her earrings as singles, encouraging wearers to buy just one, or to mix and mismatch their pairs. Louis François Cartier must be spinning in his grave. But Delettrez's rule-breaking is what makes her work so arresting. Certainly that first piece drew attention. "I started to wear it and I kind of had some special requests from family, friends," she recalls. "Then I gave birth in August, and in October I presented at Colette." Colette being the arty concept store in Paris that young designers kill to be stocked by.

Delettrez's work was an instant hit – she's still stocked there five years later, cult retailers such as Colette and Dover Street Market now sitting alongside heavyweight department stores and luxury boutiques such as New York's Saks Fifth Avenue and London's matchesfashion.com. "She has, of course, an amazing heritage," says Matches' head of fashion, Natalie Kingham. "But the pieces speak for themselves – they are for a strong woman who wants her jewellery to be as individual as she is."

The success all comes across as a bit of an accident, a mistake even. Which Delettrez quite likes. "I do learn a lot from my mistakes. A lot," she states. "I always say I really like the double meaning of the root of the word 'mistake' in Italian, which is 'errore'," her Italian accent, delicate before, is suddenly rich, regal and pronounced. "Which is the same as 'errare', which means to wander, really to discover. And this, for me, is the only way actually; it's the gift of the mistake."

Delettrez's work is a compelling mix – I mention the word sacrilegious, and she smiles. "I love everything that destabilises, disorientates you, so if you see it… these are eyes but they're earrings," she says, touching a hand to an enamelled earring. "I'm a jeweller of my era, where I'm inspired by these amazing traditions but I see it through my clothes and my millennium." That makes sense when you know that she cites Tim Burton and the Renaissance anatomist Andreas Vesalius as inspirations for her more macabre pieces, yet uses materials such as Tuscan marble and Capodimonte porcelain – alongside gold, silver and gemstones – to create her jewellery.

Despite the modernity of her work, everything is made by hand, resulting in pieces that are as unique as, say, a painstakingly saddle-stitched Fendi Selleria handbag. "I am really strict and the way of making it, it has to be handmade 100 per cent. It has to be done in a certain way, the quality has to be amazing. I think the quality is one of my… obsessions, and the craftsmanship. Pieces that are made by hand, the human touch. They're all unique pieces, because no stones can be cut the same perfect way."

The obvious question, when talking to a woman designing for women, is whether in reality she's designing for herself. Delettrez looks quizzical at this. "I guess we kind of design in a more, let's say, egoistic way," she reasons. "We design for ourselves. I am my ideal… fashion body? When I design something I really just go and look for what are my needs… they're so much my personal taste." So who is her ideal client? "Strong women, of course," she begins, halting slightly. "Great with their style… I see myself maybe in this imaginary client. Kind of a shy woman… they want their look to speak, so they don't have to speak." I guess all those Schiaparelli lips really can do the talking for you.